lucid.eye

lucid.eye(N: int, M: int | None = None, k: int = 0, /, dtype: type[bool | int | float | complex] | Numeric | None = None, requires_grad: bool = False, keep_grad: bool = False, device: Literal['cpu', 'gpu'] = 'cpu') → Tensor

The eye function creates a 2D tensor with ones on the diagonal and zeros elsewhere.

Function Signature

def eye(
    N: int,
    M: int | None = None,
    k: int = 0,
    dtype: Any = np.float32,
    requires_grad: bool = False,
    keep_grad: bool = False,
    device: _DeviceType = "cpu",
) -> Tensor

Parameters

• N (int):

  The number of rows in the output tensor.

• M (int | None, optional):

  The number of columns in the output tensor. If None, the tensor will have shape (N, N). Defaults to None.

• k (int, optional):

  The index of the diagonal. A value of 0 refers to the main diagonal, k > 0 refers to an offset above the main diagonal, and k < 0 refers to an offset below it. Defaults to 0.

• dtype (Any, optional):

  The data type of the elements in the tensor. Defaults to np.float32.

• requires_grad (bool, optional):

  If True, the resulting tensor will be part of the computation graph and capable of tracking gradients. Defaults to False.

• keep_grad (bool, optional):

  If True, the gradient history will be preserved even if the tensor does not require gradients. Defaults to False.

Returns

• Tensor:

  A 2D tensor with ones on the specified diagonal and zeros elsewhere.

Example

>>> import lucid
>>> e = lucid.eye(3)
>>> print(e)
Tensor([[1. 0. 0.]
        [0. 1. 0.]
        [0. 0. 1.]])

You can specify the number of columns and the diagonal offset:

>>> e = lucid.eye(3, 5, k=1)
>>> print(e)
Tensor([[0. 1. 0. 0. 0.]
        [0. 0. 1. 0. 0.]
        [0. 0. 0. 1. 0.]])

Note

• The eye function is useful for creating identity matrices or related structures for linear algebra and initialization tasks.

• Supports creating rectangular tensors and customizing the diagonal index.